1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to methods for 2-D inversion of induction logging data obtained with transverse induction logging tools.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that, when properly interpreted, are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p.148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
U.S. Pat. No. 5,452,761 to Beard et al. having the same assignee as the present application and the contents of which are fully incorporated herein by reference, discloses an apparatus and method for digitally processing signals received by an induction logging tool having a transmitter and a plurality of receivers. An oscillating signal is provided to the transmitter, which causes eddy currents to flow in a surrounding formation. The magnitudes of the eddy currents are proportional to the conductivity of the formation. The eddy currents in turn induce voltages in the receivers. The received voltages are digitized at a sampling rate well above the maximum frequency of interest. The digitizing window is synchronized to a cycle of the oscillating current signal. Corresponding samples obtained in each cycle are cumulatively summed over a large number of such cycles. The summed samples form a stacked signal. Stacked signals generated for corresponding receiver coils are transmitted to a computer for spectral analysis. Transmitting the stacked signals and not all the individually sampled signals, reduces the amount of data that needs to be stored or transmitted. A Fourier analysis is performed of the stacked signals to derive the amplitudes of in-phase and quadrature components of the receiver voltages at the frequencies of interest. From the component amplitudes, the conductivity of the formation can be accurately derived.
A limitation to the electromagnetic induction resistivity well logging instruments such as that discussed in Beard is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art, these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
U.S. Pat. No. 6,147,496 to Strack et al. teaches the use of an induction logging tool in which at least one transmitter and at least one receiver are oriented in orthogonal directions. By operating the tool at two different frequencies, it is possible to substantially reduce the effect of invasion and to determine the orientation of the tool to the bedding planes.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the xe2x80x9cGupta patentxe2x80x9d), the contents of which are fully incorporated here by reference, discloses a method for determination of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to a one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
Co-pending U.S. patent application Ser. No. 09/676,097 by Kriegshauser et al, the contents of which are fully incorporated herein by reference, teaches a method for determining an applying shoulder bed corrections to logging measurements made with a transverse induction logging tool. Layer boundaries are determined from the measurements. These are combined with horizontal and vertical resistivities obtained by a whole space anisotropic inversion to give a layered model. Preferably, a Lanczos iterative procedure is used for the inversion. The shoulder bed correction for each layer is derived based upon a difference between a 1-D synthetic response of the model and a whole space response of the model at that layer. The shoulder bed correction is applied to the data and the inversion procedure is repeated. This procedure is repeated in an iterative manner until a difference between the shoulder bed corrected measurements at the center of each of the layers and a synthetic response to a whole space model at the center of each of the layers is below a predetermined threshold.
Kriegshauser teaches the use of a multicomponent induction logging tool in which five components of the magnetic field as shown in FIG. 1. This tool which is marketed under the name 3DEX(trademark) by Baker Hughes Inc., measures three principal components Hxx, Hyy, Hzz and two cross-components Hxy and Hxz. The measured data from 3DEX(trademark) tool are unfocused and thus inversion is necessary in interpreting the 3DEX(trademark) data.
Only a few authors have attempted to invert borehole EM logging data to resolve anisotropic formation. Gupta et al. and Kriegshauser et al. have developed various inversion methods, including whole space inversion, radial 1D inversion, and vertical 1D inversion, to resolve anisotropic formations. EM logging data, however, are subject to borehole, shoulder, and invasion effects. The drilling mud coupled with the high pressure during the drilling process can create a flushed zone around the borehole that can be as thick as several meters. The approximate correction for borehole and shoulder effects using radial 1D and vertical 1D inversions alternatively in Kriegshauser et al., works reasonably well in most cases but these approximate corrections may not lead to satisfactory solutions in complicated situations such as high resistivity contrast and thin layers.
Additionally, different tools have different vertical resolutions and they respond differently to the earth models. Separate interpretations of multi-component induction tool and HDIL data, therefore, can lead to different and sometimes inconsistent results.
There is a need for a method of consistent interpretation of HDIL and 3DEX data to obtain anisotropic resistivities of the subsurface along with anisotropic resistivities of the invaded zone. The present invention satisfies this need.
A multi-component electromagnetic logging tool is used for obtaining multi-component measurements indicative of anisotropic resistivities of the subsurface. An initial model of the subsurface, including horizontal and vertical resistivities and parameters of an invaded zone around a borehole, is defined. A forward modeling program is used to obtain expected responses of the multi-component tool based on the initial model. An iterative procedure is used to update the model and minimize an objective function related to the mismatch between the model output and the multi-component measurements. The objective function also includes a model objective function to stabilize the inversion process. The initial model for the inversion may be obtained from other measurements, such as an array logging tool.
In another embodiment of the invention, the data from the multi-component logging tool are inverted jointly with data from an array logging tool. This joint interpretation can give results superior to those obtained from the inversion of the multi-component data alone. The improvement is noticeable in estimation of the invaded zone parameters.